Many triangulated odd-dimensional spheres

Eran Nevo*, Francisco Santos, Stedman Wilson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


It is known that the (Formula presented.) -sphere has at most (Formula presented.) combinatorially distinct triangulations with n vertices, for every (Formula presented.). Here we construct at least (Formula presented.) such triangulations, improving on the previous constructions which gave (Formula presented.) in the general case (Kalai) and (Formula presented.) for (Formula presented.) (Pfeifle–Ziegler). We also construct (Formula presented.) geodesic (a.k.a. star-convex) n-vertex triangulations of the (Formula presented.) -sphere. As a step for this (in the case (Formula presented.)) we construct n-vertex 4-polytopes containing (Formula presented.) facets that are not simplices, or with (Formula presented.) edges of degree three.

Original languageAmerican English
Pages (from-to)737-762
Number of pages26
JournalMathematische Annalen
Issue number3-4
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


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